New exact solutions of nontraveling wave and local excitation of dynamic behavior for GGKdV equation

For GGKdV equation, solutions of the compatible KdV equation are obtained by using CKdVE method, and Lie point symmetry group of the equation is also obtained. Further, some new exact non-traveling wave solutions are obtained by using the equivalent transformation method and elliptic function method on solving the corresponding symmetric reduction equation, and local excitation modes of three kinds of solutions under three different groups of parameters are presented. Finally, the integrability in the sense of the CkdVE and the Lie Symmetric are proved, which shows the effectiveness of the organic combination of various kinds of nonlinear analytical methods. This CkdVE method communicated the mathematical relations of different nonlinear models. It is a new bridge between the known and unknown solutions of the nonlinear partial differential equations, and it is a new way to explore complex nonlinear complex phenomena.